Gear-shaped precision-working tools which have geometrically defined cutting edges on their tooth flanks have been known for a long time and are generally identified as shaving gears. Gear-shaped precision-working tools identified as honing cutters, hard shaving cutters or the like are also known, the flanks of which have an abrasive surface.
It is known from DE-PS 970 027 (corresponds to U.S. Pat. No. 3,180,227) to select, in order to achieve an optimum shaving result, the dimensions (module, pressure angle, number of teeth, profile displacement factor, pitch angle, tooth addendum height) of a shaving gear in such a manner that, within the paths of contact or lengths of action with the workpiece, an even number of tooth flanks always successively and simultaneously engage one after the other and that the pitch point divides the lengths of action at the transition point between two path lengths corresponding with such states of contact.
A shaving gear is reground during its lifetime, depending on its use, approximately 10 to 15 times, with at least 0.03 mm being removed from each tooth flank or, in the case of significant wear, even up to 0.1 mm is removed. Since the original pitch angle is maintained during the regrinding, the profile displacement factor changes toward a negative. This profile displacement factor, which changes continuously during the lifetime of the shaving gear, has the result that the "state of symmetry" known from DE-PS 970 027 is, as a rule, only achieved during a grinding state of the shaving gear. In practice one proceeds in designing a shaving gear in such a manner that it lies above the state of symmetry when it is new, thus does not yet achieve an optimum shaving result, but achieves an optimum shaving result only once it has been reground several times; however, the shaving result worsens with each further regrinding until the worn or used-up state of the shaving gear has been reached.